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Question-188455




Question Number 188455 by Rupesh123 last updated on 01/Mar/23
Answered by HeferH last updated on 02/Mar/23
Commented by HeferH last updated on 02/Mar/23
Prove that: x = 2(a + b) − a   1. ((c + d)/c) = (x/a)   2. (d/(c + d)) = ((2b)/x)   3. (d/c)∙((c+d)/(c+d)) = ((2b)/a)   4. 1 + ((2b)/a) = (x/a)        a + 2b = x        a + a + 2b − a = x         2(a + b) − a = x ✓
$${Prove}\:{that}:\:{x}\:=\:\mathrm{2}\left({a}\:+\:{b}\right)\:−\:{a} \\ $$$$\:\mathrm{1}.\:\frac{{c}\:+\:{d}}{{c}}\:=\:\frac{{x}}{{a}} \\ $$$$\:\mathrm{2}.\:\frac{{d}}{{c}\:+\:{d}}\:=\:\frac{\mathrm{2}{b}}{{x}} \\ $$$$\:\mathrm{3}.\:\frac{{d}}{{c}}\centerdot\frac{\cancel{{c}+{d}}}{\cancel{{c}+{d}}}\:=\:\frac{\mathrm{2}{b}}{{a}} \\ $$$$\:\mathrm{4}.\:\mathrm{1}\:+\:\frac{\mathrm{2}{b}}{{a}}\:=\:\frac{{x}}{{a}} \\ $$$$\:\:\:\:\:\:{a}\:+\:\mathrm{2}{b}\:=\:{x} \\ $$$$\:\:\:\:\:\:{a}\:+\:{a}\:+\:\mathrm{2}{b}\:−\:{a}\:=\:{x}\: \\ $$$$\:\:\:\:\:\:\mathrm{2}\left({a}\:+\:{b}\right)\:−\:{a}\:=\:{x}\:\checkmark \\ $$
Commented by Rupesh123 last updated on 02/Mar/23
Nice solution!

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